Quantum field theory

Abstract

Quantum field theory describes the interactions of particle in terms of the interaction between fields, with the particles interpreted as quanta of the fields. In the absence of any interactions, the fields are defined by their Lagrangian, and each field satisfies appropriate field equations that follow from the Euler-Lagrange equations applied to the Lagrangian. Interactions are determined by interaction Lagrangians, that involve two or more fields. In a diagrammatic approach, each interaction is described by a vertex, and interactions with two or more vertices involve exchange of a virtual particle, described by the propagator for the field. The propagator for the field is the Green's function for the field equation, and a particle corresponds to a pole in the propagator. Quantum electrodynamics (QED) is the quantum field theory for the interaction between the Dirac field, whose quanta are electrons and positrons, and the electromagnetic (EM) field, whose quanta are photons. Scalar electrodynamics (SED) is the counterpart of QED in which the particles are assumed to be spinless, satisfying the Klein-Goron equation rather than Dirac's equation. In the simplest generalization of QED to quantum plasmadynamics (QPD), the electromagnetic field is replaced by the self-consistent field in a plasma. The classical wave wave fields corresponding to each natural mode, M, of the medium, are quantized, so that the mode of a wave quantum or 'photon' needs to be specified. © 2008 Springer-Verlag New York.